Executive Summary : | In recent years, the interplay between ring structure and graph structure are studied by many researchers. One of the important graphs constructed from finite groups viz Cayley graphs. Cayley graphs have been well studied as they are used as an underlying network for routing problems in parallel computing. Another important construction of graphs from commutative rings is the zero-divisor graphs of a commutative ring. In these attempts, researchers define a graph whose vertices are a set of elements, or a set of ideals in the ring and edges are defined with respect to an algebraic condition on the elements of the vertex set. Certain well-studied classes of graphs are zero-divisor graphs, total graphs, annihilating graphs, comaximal graph, unit graph, Cayley graph, Jacobson graph, generalized total graph, Cayley sum graph and trace graph of matrices from commutative rings. These graphs constructed from commutative rings help the researchers to study the algebraic properties of commutative rings using graph theoretical tools. |
